# Message #1413

From: Eduard <baumann@mcnet.ch>

Subject: Re: The 3 slice pentachoron

Date: Tue, 15 Feb 2011 20:59:21 -0000

Thanks for the answer.

— In 4D_Cubing@yahoogroups.com, "Matthew" <damienturtle@…> wrote:

>

> With a little thought, the {3,3,3}3 puzzle (this can serve to check I’m thinking of the correct puzzle) is fairly easy to solve. The octahedra located around a vertex are one piece and can easily be orientated correctly, and the tetrahedra at each vertex are equivalent to the trivial tips on a pyraminx and thus are easy to solve in a similar manner, although you know all this already. This leaves the 10 edges which can be 3-cycled using basically the same 4-move sequence which applies on a normal pyraminx. This allows the sequence which flips 2 edges on a pyraminx to also apply. A slight change in 4D is similar to one found on the 3x3x3x3: you can have a single edge with incorrect orientation. Think about the previous sequence to flip 2 edges in place (switching 2 stickers on each, to clarify). Perform this, then perform a single twist about an edge to change the stickers being swapped on one of those edges. Then repeat (or undo) the flipping sequence and undo the edge twist. I will upload a log file demonstrating this after posting. Any more questions, just ask (I sometimes don’t explain things well).

>

> Matt

>

> PS. Funny coincidence, my Meffert’s Professor Pyraminx arrived today, so I might do the {3,3,3}5 for fun sometime soon. When/if I do, I can write a short guide if there is enough interest, although I feel that most of the fun in this group is covering new ground and solving puzzles with no tutorial to follow.

>

> — In 4D_Cubing@yahoogroups.com, "Eduard" <baumann@> wrote:

> >

> >

> > I asked in this forum for instructions for the pentachoron (3 slices).

> >

> > Since I got no reaction I think that these instructions do not exist. At

> > least not for a layered solution (as Roice’s for the magic cube). This

> > is not astonishing because the pentachoron beeing smaller (only 5 cells

> > compared with the 8 cells of the magic cube) seems to be more ensnared.

> > Reading (watching, playing) the log files from R.Durka I can’t learn

> > anything. Does he use computer aid?

> >

> > We can distinguish the following technics (1) fully by hand, (2) by hand

> > and macros, (3) with heavy computer aid. I’m doing (2).

> >

> > Without any macros and commutators you can do the 5 faces with 4

> > differently colored octahedra. Then the 5 fourcolored corners can be

> > done with slice 3 twists only.

> > After that you have the hard core of the job to be done: the 10

> > threecolored edges. For the moment I have established a 3-cycles across

> > an edge, a 3-cycle in a face and a 3-cycle around a vertex. I have also

> > a concept for a sequence which mirrors two edges in their place. I need

> > also a sequence to turn two edges in their place. All these sequences

> > work with slice 2 twists of course.

> >

>